2009 Fiscal Year Final Research Report
Differential geometric researches on surfaces in a space of constant curvature and their singularities
| Project/Area Number |
18540096
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Tokyo Denki University |
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Principal Investigator |
KOKUBU Masatoshi Tokyo Denki University, 工学部, 教授 (50287439)
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| Co-Investigator(Kenkyū-buntansha) |
IRIE Hiroshi 東京電機大学, 未来科学部, 講師 (30385489)
KOBAYASHI Shimpei 弘前大学, 大学院・理工学研究科, 助教 (40408654)
ROSSMAN Wayne 神戸大学, 大学院・理学研究科, 教授 (50284485)
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| Project Period (FY) |
2006 – 2009
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| Keywords | 微分幾何 / 平均曲率 / ガウス曲率 / 特異点 |
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| Research Abstract |
We studied surfaces in a three-dimensional manifold of constant negative curvature, called the hyperbolic space, requiring them to have good properties from the differential-geometric viewpoint. (Note that the hyperbolic space has interesting features beyond our common sense, e.g., a single hyperbolic line has infinitely many parallels.) We clarified the asymptotic behavior of ends of flat surfaces admitting singularities. Concerning linear Weingarten surfaces, we had a global representation formula, criterion for the shape of singularities, the orientability and co-orientability, and so on.
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Research Products
(11 results)
